Ferris Wheel - Trigonometric Function

1. The problem statement, all variables and given/known data
At Canada's Wonderland, a thrill seeker can ride the Xtreme Skyflyer. This is essentially a large pendulum of which the rider is the bob. The height of the rider is given for various times:

Time(s) 0 1 2 3 4 5 6 7 8 9
Height(m) 55 53 46 36 25 14 7 5 8 15

Find the amplitude, period, vertical translation, and phase shift for this function. [Note: that the table does not follow the bob through one complete cycle, s

However, because this ride works as a pendulum, one cycle will be completed when there are 2 highs and 2 lows. So the bob starts at a height of 55 metres; it will then reach a low of 5 metres; it will (hypothetically) reach a height until it runs out of speed; it will then (hypothetically) return to the minimum height of 5 metres; and then, finally it will return to its start position. That is the completion of 1 cycle in a pendulum.

Because the graph is incomplete, we have just one maximum and one minimum. The maximum starts at 55 metres, and then there is a minimum at 5 metres. Therefore, we have only completed 1/4 of the cycle at 7 seconds. Roughly, a complete cycle will take 28 seconds.

Therefore Period= 2pie/b

which becomes:
28 seconds = 2pie/b
28=360/b
b=360/28
b=12.86

So the "b" value is 12.86.

To find the value of "c", I will plug in a co-ordinate value into the equation. Let us take the co-ordinate (3, 36)